くだらねぇ問題スレ ver.3.141592653589793238
56 名前：ななし 投稿日：2002/06/26(水) 19:50
Solve[a x^4 + b x^3 + c x^2 + d x + e == 0, x]
x -> -(b/(4*a)) - 1/2*Sqrt[b^2/(4*a^2) - (2*c)/(3*a) + (2^(1/3)*(c^2 - 3*b*d +
12*a*e))/ (3*a*(2*c^3 - 9*b*c*d + 27*a*d^2 + 27*b^2*e - 72*a*c*e + Sqrt[-4*(c^2 -
3*b*d + 12*a*e)^3 + (2*c^3 - 9*b*c*d + 27*a*d^2 + 27*b^2*e - 72*a*c*e)^2])^(1/3))
+ 1/(3*2^(1/3)*a)* (2*c^3 - 9*b*c*d + 27*a*d^2 + 27*b^2*e - 72*a*c*e +
Sqrt[-4*(c^2 - 3*b*d + 12*a*e)^3 + (2*c^3 - 9*b*c*d + 27*a*d^2 + 27*b^2*e - 72*
a*c*e)^2])^(1/3)] - 1/2*Sqrt[b^2/(2*a^2) - (4*c)/(3*a) - (2^(1/3)*(c^2 - 3*b*d +
12*a*e))/ (3*a*(2*c^3 - 9*b*c*d + 27*a*d^2 + 27*b^2*e - 72*a*c*e + Sqrt[-4*(c^2 -
3*b*d + 12*a*e)^3 + (2*c^3 - 9*b*c*d + 27*a*d^2 + 27*b^2*e - 72*a*c*e)^2])^(1/3))
- 1/(3*2^(1/3)*a)* (2*c^3 - 9*b*c*d + 27*a*d^2 + 27*b^2*e - 72*a*c*e +
Sqrt[-4*(c^2 - 3*b*d + 12*a*e)^3 + (2*c^3 - 9*b*c*d + 27*a*d^2 + 27*b^2*e - 72*
a*c*e)^2])^(1/3) - (-(b^3/a^3) + (4*b*c)/a^2 - (8*d)/a)/
(4*Sqrt[b^2/(4*a^2) - (2*c)/(3*a) + (2^(1/3)*(c^2 - 3*b*d + 12*a*e))/
(3*a*(2*c^3 - 9*b*c*d + 27*a*d^2 + 27*b^2*e - 72*a*c*e + Sqrt[ -4*(c^2 -
3*b*d + 12*a*e)^3 + (2*c^3 - 9*b*c*d + 27*a*d^2 + 27*b^2* e -
72*a*c*e)^2])^(1/3)) + 1/(3*2^(1/3)*a)*(2*c^3 - 9*b*c*d +
27*a*d^2 + 27*b^2*e - 72*a*c*e + Sqrt[ - 4*(c^2 - 3*b*d + 12*a*e)^3 + (2*c^3 -
9*b*c*d + 27*a*d^2 + 27*b^2*e - 72*a*c*e)^2])^(1/3)])]
>>546 別スレにあったこの４次方程式の解をキミにプレゼントだ
Solve[a x^4 + b x^3 + c x^2 + d x + e == 0, x]
x -> -(b/(4*a)) - 1/2*Sqrt[b^2/(4*a^2) - (2*c)/(3*a) + (2^(1/3)*(c^2 - 3*b*d +
12*a*e))/ (3*a*(2*c^3 - 9*b*c*d + 27*a*d^2 + 27*b^2*e - 72*a*c*e + Sqrt[-4*(c^2 -
3*b*d + 12*a*e)^3 + (2*c^3 - 9*b*c*d + 27*a*d^2 + 27*b^2*e - 72*a*c*e)^2])^(1/3))
+ 1/(3*2^(1/3)*a)* (2*c^3 - 9*b*c*d + 27*a*d^2 + 27*b^2*e - 72*a*c*e +
Sqrt[-4*(c^2 - 3*b*d + 12*a*e)^3 + (2*c^3 - 9*b*c*d + 27*a*d^2 + 27*b^2*e - 72*
a*c*e)^2])^(1/3)] - 1/2*Sqrt[b^2/(2*a^2) - (4*c)/(3*a) - (2^(1/3)*(c^2 - 3*b*d +
12*a*e))/ (3*a*(2*c^3 - 9*b*c*d + 27*a*d^2 + 27*b^2*e - 72*a*c*e + Sqrt[-4*(c^2 -
3*b*d + 12*a*e)^3 + (2*c^3 - 9*b*c*d + 27*a*d^2 + 27*b^2*e - 72*a*c*e)^2])^(1/3))
- 1/(3*2^(1/3)*a)* (2*c^3 - 9*b*c*d + 27*a*d^2 + 27*b^2*e - 72*a*c*e +
Sqrt[-4*(c^2 - 3*b*d + 12*a*e)^3 + (2*c^3 - 9*b*c*d + 27*a*d^2 + 27*b^2*e - 72*
a*c*e)^2])^(1/3) - (-(b^3/a^3) + (4*b*c)/a^2 - (8*d)/a)/
(4*Sqrt[b^2/(4*a^2) - (2*c)/(3*a) + (2^(1/3)*(c^2 - 3*b*d + 12*a*e))/
(3*a*(2*c^3 - 9*b*c*d + 27*a*d^2 + 27*b^2*e - 72*a*c*e + Sqrt[ -4*(c^2 -
3*b*d + 12*a*e)^3 + (2*c^3 - 9*b*c*d + 27*a*d^2 + 27*b^2* e -
72*a*c*e)^2])^(1/3)) + 1/(3*2^(1/3)*a)*(2*c^3 - 9*b*c*d +
27*a*d^2 + 27*b^2*e - 72*a*c*e + Sqrt[ - 4*(c^2 - 3*b*d + 12*a*e)^3 + (2*c^3 -
9*b*c*d + 27*a*d^2 + 27*b^2*e - 72*a*c*e)^2])^(1/3)])]
>>546 別スレにあったこの４次方程式の解をキミにプレゼントだ
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